Full paper in PDF:
$%C. Hayashi and K. Shimokawa, Heegaard splittings of the pair of the solid torus and the core loop, Rev. Mat. Complut. 14 (2001), no. 2, 479501.%$

Heegaard Splittings of the Pair of the Solid Torus and the Core Loop
Chuichiro HAYASHI and Koya SHIMOKAWA
Department of Mathematics
Faculty of Science
Gakushuin University
1-5-1 Mejiro Toshima-ku Tokyo, 171 — Japan
Graduate School of Information Sciences
Tohoku University
2-1-1 Katahira Aoba-ku Sendai, 980-8577 — Japan

Received: March 20, 2000
Revised: December 4, 2000

ABSTRACT

We show that any Heegaard splitting of the pair of the solid torus (    2   1
~= D  × S  ) and its core loop (an interior point    1
×S  ) is standard, using the notion of Heegaard splittings of pairs of 3  -manifolds and properly imbedded graphs, which is defined in this paper.

2000 Mathematics Subject Classification: 57M25, 57N10.